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A 3 digit number is randomly formed, find the probability than it's common divisor with 36 is only 2.?
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A 3 digit number is randomly formed, find the probability than it's co...
Probability of Common Divisor with 36 being only 2
Understanding the Problem
When a number has a common divisor of 2 with 36, it means it is an even number but not divisible by 4 or 9.
Finding the Total Possible 3-Digit Numbers
There are 900 possible 3-digit numbers (from 100 to 999).
Finding the Total Numbers Divisible by 2
There are 450 numbers that are divisible by 2 (every other number in the sequence).
Finding the Numbers Divisible by 4 and 9
There are 225 numbers divisible by 4 (every fourth number in the sequence) and 100 numbers divisible by 9 (numbers ending in 0 or 8).
Finding the Numbers with Common Divisor of 2 with 36
Numbers divisible by 4 and 9 are also divisible by 36, so we need to subtract these from the total numbers divisible by 2.
Numbers divisible by 4 and 9 = 225 + 100 - 25 (numbers divisible by both 4 and 9)
Total numbers with common divisor of 2 with 36 = 450 - 25 = 425
Calculating the Probability
Probability = Number of favorable outcomes / Total possible outcomes
Probability = 425 / 900
Probability = 17 / 36
Therefore, the probability that a randomly formed 3-digit number has a common divisor with 36 of only 2 is 17/36.
Understanding the Problem
When a number has a common divisor of 2 with 36, it means it is an even number but not divisible by 4 or 9.
Finding the Total Possible 3-Digit Numbers
There are 900 possible 3-digit numbers (from 100 to 999).
Finding the Total Numbers Divisible by 2
There are 450 numbers that are divisible by 2 (every other number in the sequence).
Finding the Numbers Divisible by 4 and 9
There are 225 numbers divisible by 4 (every fourth number in the sequence) and 100 numbers divisible by 9 (numbers ending in 0 or 8).
Finding the Numbers with Common Divisor of 2 with 36
Numbers divisible by 4 and 9 are also divisible by 36, so we need to subtract these from the total numbers divisible by 2.
Numbers divisible by 4 and 9 = 225 + 100 - 25 (numbers divisible by both 4 and 9)
Total numbers with common divisor of 2 with 36 = 450 - 25 = 425
Calculating the Probability
Probability = Number of favorable outcomes / Total possible outcomes
Probability = 425 / 900
Probability = 17 / 36
Therefore, the probability that a randomly formed 3-digit number has a common divisor with 36 of only 2 is 17/36.
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A 3 digit number is randomly formed, find the probability than it's common divisor with 36 is only 2.?
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A 3 digit number is randomly formed, find the probability than it's common divisor with 36 is only 2.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A 3 digit number is randomly formed, find the probability than it's common divisor with 36 is only 2.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 3 digit number is randomly formed, find the probability than it's common divisor with 36 is only 2.?.
A 3 digit number is randomly formed, find the probability than it's common divisor with 36 is only 2.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A 3 digit number is randomly formed, find the probability than it's common divisor with 36 is only 2.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 3 digit number is randomly formed, find the probability than it's common divisor with 36 is only 2.?.
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